CCE Series <br> NiathenatiGs Term <br> tive <br> amidea <br> CCE Series <br> Summative Assessment <br> MATHEMATICS <br> (Continuous and ComprehensiveEvaluation) <br> Term 1: Summative Assessment-1 <br> Formative Assessment- 1&2 <br> Class IX <br> Model Question Papers <br> O Multiple Choice Questions <br> O Short Answer QuestionsS <br> OLong Answer Questions <br> O Project <br> Formative Assessment <br> O Activity <br> O Rapid Fire Quiz <br> SucceSS <br> OOral Questions <br> O Paper Pen Test <br> O Multipe Choice Quetions <br>
CCE Series <br> Mathematics <br> (ContinuOus and Comprehensive Evaluation] <br> Term 1: Summative Assessment- 1 <br> TSummative Assessment <br> -Model Question Papers <br> -Multiple Choice Questions <br> Formative Assessment - 1 & 2 <br> -Short Answer Questions <br> -Long Answer Questions <br> IFormative Assessment <br> -Project <br> -Activity <br> -Rapid Fire Quiz <br> -Oral Questions <br> Paper Pen Test <br> -Multiple Choice Questions <br> KGlobgl <br> Publicotions Pvt. Ltd. <br> gode.N.!ns <br> Class. <br> IX <br> TIÍdea <br>
Contents <br> UNT- I Number Syxtew <br> Sumumative and oatve Asnessnwnt <br> I., Roal Numtrs <br> UNIT- I| Algebra <br> 378S3 5 <br> UNIT ||l Geometry <br> 8, lInrohuetion to Buclid's (Geomery <br> onnaive Anesment <br> t. Lines and Angls. <br> 5. Triangles.... <br> lomaive :\seuct <br> 'TERM-| <br> UNIT - IV Coordinate Geometry <br> 6. Coordinate Geometiry <br> tomative Avsessnent <br> UNIT -V Mensuration <br> 7. Area ofriangks-Heron's lormula. <br> Formative Asessoent <br> LatestCBSE Sample aper <br> Model Question Vapers (Sokel) . <br> Model Qucstion lapers (Unsolve).... <br> )) <br> 58 <br> 62 <br> 77 <br> 8-1 <br> .96 <br> 103 <br> I18 <br> 130 <br> 135 <br> 1-45 <br> I88 <br>
Time: 3 hours <br> General Instructions: <br> 1. Al questions are comþulsory. <br> 1ne question paper consists of 34 auestions divided into 4 sctions. A. B. Cand D. Section -A comfprises of 8 <br> questto5 of 1 mark each. Section - B Combrises of 6 estions of 2 marks each. Section-G comprses of 10 <br> uestions of 3 marks each and Section-D comprises of 10 questions of 4 marks each. <br> D. eslon numbers 1 to 8 in Sectiom-A are multible choice questions where you are to select one COTTea opLOTn Od of <br> the given four. <br> 5. Use of calculators is not permitted. <br> Model Question Paper (Unsolved) -1 <br> 1. There is no overall choice. However, internal choice has been trovided in 1 question of twO marks, 3 questions of <br> Zhree marks each and 2 questions offour marks each. You have to attempt only one of lhe alernattves tn all such <br> questions. <br> (a) terminating <br> Summative Assessment - I <br> Question numbers I to 8 carry l mark each. <br> I. Decimal representation of a rational number cannot be <br> (c) non-terminating repeating <br> (a) 0 <br> Mathematics <br> (a) 1 <br> 2. IfP(x)= *²-2/2x +1, then P (2/2) is equal to <br> (a) 100 <br> 3. If +2=-1 (*,y+0), the value ofx'-y° is <br> (c) J24 cm <br> 4. The value of (525)* -(475) is <br> (b) I <br> (a) 316 cm² <br> (c) 296 cm? <br> (6) -1 <br> (b) 10000 <br> Section -A <br> 6. The area of trapezium in Fig. I is <br> (b) 48 cm <br> (d) 4 cm <br> 5. An isosceles right triangle has area 8 cm². The length of its hypotenuse is <br> (a)J32 cm <br> (b) 306 cm? <br> (d) 286 cm? <br> (b) non-terminatúng <br> (d) non-terminating non-repeating <br> (c) 4/2 <br> Maximum Marks: 90 <br> (c) 0 <br> (c) 50000 <br> 9 cm <br> () 8/2 +1 <br> (d) 100000 <br> 28 cm <br> 40 cmn: <br> Fig. 1 <br> ) <br> 15 cm <br> VKGotat pbhcatans P e <br>
7. Axioms are assumed <br> (a) universal I truths in all branches of Mahemaics <br> (c) theorcms <br> truc? <br> (a) DF =5 cm, ZT = 60° <br> (c) DE = 5cm, ZF= 60° <br> 8. It is giventhat MBCe AFDE and AB = 5 cm, ZB=40°and A =80°Then which of the following is <br> false. Justily your answer. <br> Ouestion numbers 9 to 14 carry 2 marks each. <br> /147 <br> 9. - is not a rational number as y47 and w75 are not integers. State whether the statement is true or <br> /75 <br> 10. Without actually calculating the cubes, find the value of 48-30- 183. <br> 1 Ifx +l is a factor of ax +**-2x +4a-9, find the value of a. <br> OR <br> In Fig. 3, if l|| m, then find x. <br> Simplify: <br> 3 <br> 19. Solve the equation a –1l5=25 and state which axiom do you have. <br> 13, In Fig. 2, what value of x will make POR a straight line? <br> (6) DF =5 cm, ZE = 60° <br> -2 <br> (d) DE = 5 cm, ZD = 40° <br> 93x 27 2 <br> 36 x3 3 <br> SR <br> OR <br> A (0, -3), B(3, 4), C(5, 0), D(-2, 2) <br> (4x-36)° <br> 14. Which of the following points will lie on x-axis or y-axis? <br> ©VK Global Publications Pvt. Ltd. <br> Section- B <br> Flg.2 <br> (b)universal truths specific to geometry <br> (d) definitions <br> Question numbers 15 to 24 carry 3 marks each.stv atete <br> 15. Find three rational numbers between and <br> 16. Express 0.123 in the form of. <br> (3x + 20)° <br> 17. Using an identity evaluate (998)° <br> Model Question Papers <br> 3 <br> Section -C <br> 9 <br> 3 <br> 189 <br> 44° <br> Flg. 3 <br>
190 <br> Mathematics IX : Term - I <br> 18. Find the valuc of k so that 2x-lbea factor of8z4 + 4y-16z+10z * <br> Factorise: 1-64a -12a + 48a <br> 19. In Fig. 4, if AC= BD, using an Euclid's axiom show that AB =D. <br> OR <br> 20. In Fig. 5, BA||ED andBCl|EF. Show that ZABC= DEF., <br> 25. <br> In Fig. 6, if PQ||RS, ZMXQ = 135° and ZMYR = 40°, find XMY. B <br> OR <br> P <br> R <br> 21. In Fig. 7, D and E are points on side BC of a AABC such that BD = CE and <br> AD = AE. Show that AABD= AACE. <br> V2+1 <br> If x = <br> /2 -1 <br> 22. In Fig. 8, PQ = PR and ZO= ZR. Prove that APOS APRT. <br> (b) four times its supplement. <br> 23. Find the measure of an angle which is <br> 26. Simnplify: <br> (a) one-fourth of its complement. <br> Fig. 4 <br> 40° <br> and y = <br> Fig. 6 <br> Question numbers 25 to 34 carry 4 marks each. <br> 7/3 <br> V10 +/3 <br> /2-1 <br> /2 +1 <br> OR <br> Fig. 8 <br> 2/5 <br> 24. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. Find the <br> area of the triangle. <br> S <br> Ifa =5-2/6, then findthe value of Va <br> Section - D <br> R <br> 3/2 <br> J6 +V5 V15 +32 <br> find the value ofx*+y +xy. <br> B <br> D <br> tt <br> Fig.7 <br> m <br> OVK Global Publications Pv LId <br>
27. Find the product <br> (* -2y-z)(*? +4y'+z² +2ry +xz -2yz) <br> 28. Factorise: (2r +3)3 -(2x -3y) <br> OR <br> Factorise: x* +2* y -2y-1 <br> 29. Ifz +=83, find the value of z <br> 30. From the Fig. 9, answer the following: <br> (i) Coordinates of point C. <br> (ü) The point identified by the coordinates (-3, -7). <br> (iii) The abscissa of the point E. <br> (iv) The ordinate of the point F. <br> (u) Coordinates of point O. <br> (vi) The quadrant in which point G lies. <br> Fig. 9 <br> (vin) The perpendicular distance of the point A from the x-axis. <br> OF <br> (vii) The perpendicular distance of the point B from the y-axis. <br> 31. Prove that the sum of the angles of a triangle is 180°. <br> VK Global Publications Pvt. Ltd. <br> Model Question Papers <br> 191 <br> S2. In a AABC, the angle bisectors of the B and 2C meet at 0. IfZA =60°, then find the value ofZBOC. <br> 33. A transversal intersect two parallel lines. Prove that the bisectors ofany pair of correspondingangles so <br> formed are parallel. <br> Ot. Ifthe bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles. <br>
Time: 3 hours <br> General Instructions: As given in ModelQuestion Paper (Unsolved)l <br> Question numbers 1 to 8 carry <br> 1. The value of 19.999.... <br> 10 <br> 4. <br> 2 <br> (a) 21 <br> (a) 24 <br> Model Question Paper (Unsoved)-2 <br> Summative Assessment - ! <br> 2. Which of the following is a polynomial? <br> (a) ** <br> 2 <br> (a) <br> (a) 40/15 cm² <br> 3. Ifx-20 is divided by x +1, the remainder is <br> -y² <br> 4 <br> (b) <br> cm? <br> Mathematics <br> If x +y=9 and *y = 20, then the value of x <br> 7. Greeks emphasised on <br> (a) inductive reasoning <br> (c) botha and b <br> l mark each. <br> 1999 <br> 1000 <br> (6) /2x -1 <br> VK Global Publications Pvt. Ltd. <br> in the form , where and g are integers and q #0 is <br> (b)21 <br> (b) 41 <br> (b) <br> 5. The sides of a triangle are 13 cm, 17 cm and 20 cm. Its area is <br> Section - A <br> (b) 20V30 cm² <br> 8. Complementary angle of 35° is <br> (a) 145° <br> (b)55° <br> 6. The area of an isosceles triangle having base x cm and equal side y cm is <br> 2 <br> *y2 <br> cm² <br> Question nunbers 9 to 14 carry 2 mnarks each. <br> (c) 2 <br> (c)x2+ <br> (c) 20 <br> (c) 81 <br> (iü) 10.124124.. <br> 3 <br> " <br> (c) 60V10 cm² <br> (c) x4y²-*² cm? <br> Section - B <br> (b) deductive reasoning <br> (c) 325o <br> Maximum Marks: 90 <br> 9. Classify the following numbers as rational or irrational with justification, <br> (i) 1.020020002.. <br> (4) <br> (a) *~1 <br> 1 <br> ir. (a) 40/30 cm² <br> (d) practical use of geometry <br> (d) -20 <br> (d) 141 <br> (a) <br> +1 <br> 2 <br> 4y-x2 <br> 4 <br> cm² <br> (d) none of these <br>
193. <br> Mathematics IX: Term -| <br> 10. Evaluate: (97)? by using an identity. <br> 11. Find the value ofk, ifx +3 is a factor of 3x + kx +6. <br> lidian geometry 1S Valia only for curved surfaces. State whether this statement is true or false. <br> Justify your answer. <br> T wo triangles ABG and DEr, AB = DE and AC = EF. Name two angles from the two triangles that <br> must be equal so that the two triangles are congruent. Give reasons for your answer. <br> 1fone angle of a triangle is greater than the sum of the other two. show that the triangle is an obtuse <br> angled triangle. <br> or on which axis each of the following points lie? <br> A(0, -5), B(-3, -3) <br> 14. In which quadrant <br> 16. Simplify: <br> Ouestion numbers l5 to 24 carry3 marks each. <br> 15. Represent: v3.5 on the number line <br> Show that <br> 3 <br> (25)2 x (243) 5 <br> 5 <br> (16)+ x(8) 3 <br> 12 <br> 17. Factorise: 8p+p². <br> 5 <br> Factorise: 3-12(2 -b) <br> X <br> 3 <br> Fig. 1 <br> 9 <br> 6 <br> P <br> OR <br> 25 <br> + <br> 19. In the Fig. 1, ifOX =XY, PX= <br> OR <br> 20. In Fig. 2, find x if AB|| CD||EF. <br> 18. Determine the value ofa for which the polynomial 2r* +3*+2ax*+3x +6 is divisible by I-2%. <br> 125 <br> 1 <br> OR <br> OR <br> =1 <br> 1 <br> Section -C <br> A< <br> XZ and 0X = PX, using Euclid's axiom, show that XY = XZ <br> C <br> 60 <br> Fig. 2 <br> B <br> 140° <br> In Fig. 3, lines XY and MN intersect at 0. If ZPOY = 90° <br> and a:b= 2:3,find c. <br> D <br> Fig. 3 <br> OVK Global Publications Pvt Ltd. <br>
21. <br> PrOve that the measure of each angle of an cquilateral riange <br> 22. In Fig. 4, ifAB||CD, 21:22 = 5:4, then find 6 <br> 6 <br> 7+3 <br> 29. <br> 23. The angles of a uriangle are in the ratio 2:3:4. Find the angles of the triangie <br> Show that: <br> Flg. 4 <br> 2 <br> 44. ind he arca of an isosccles trianle each of whose eual sides are 13 cm and whose base is 24 cm. <br> Question numbers 25 to34 carry 4 marks each. <br> 25. Ifx =- ind the value of x -2*-7x -4. <br> 2-/3 <br> 26. Ir +2/3 <br> = 4-V3 b, find a and b. <br> B <br> OR <br> Factorise: -7-8od, <br> 3-J8 8 -7 7-/6 v -/5 /5-2 <br> Section –D <br> 27. Using factor theorem, factorise the polynomial x* +*-7x-x+6. <br> OR <br> Model Question Papers <br> =5 <br> If-1 is a factor of at +-2 +6, find the values of a and b. <br> O VK Global Publications Pyt. Ltd. <br> 28. Find the product of (2x -y +3z) (4x? +y² +9z+2xy +3yz 6xz).hho Disl <br> 30. Plot the following points and write the name of the figure thus <br> obtained: <br> P(-1, 0), Q (2, 0), R (2, 3), S (-l, 5). Also find the arca of the figure <br> obtained. <br> 31. In Fig. 5,m and n are two plane mirrors perpendicular to cach other. <br> Showthat incident ray CA is parallel to relected ray BD. <br> 32. Prove that the angle between the internal bisector of one base angle <br> and thc external bisector of other is equal to one half of the vertical <br> angle. <br> m <br> D, <br> 194 <br> P <br> 33. Prove that the angles opposite to equal sides of a triangle are cqual.. a '3Dst <br> Flg. 5 <br> 34. In a triangle ABC, it is givcn thatAB = AC and the bisectors of ZB and ZCintersect at O. IfM is a point <br> on BOproduced, prove that ZMOC = ABC. <br>
Time: 3 hours <br> Coneral Instructions: As gwen tn Model Question Paper (Unsolved) 1. <br> 1 equals <br> 5 +3 <br> (a) V5-3 <br> Ouestion numbers 1 to 8 carry l mark each. <br> Model Question Paper (Unsolved) -3 <br> Summative Assessment - I <br> (a) only <br> 3. Zeroes of the polynomial 7x-1 are <br> 2. If b(x) =x+3, then p(*)+ p(-*) is equal to <br> (a) 3 <br> (6) 2x <br> (a) a +b =0 <br> 5. If2%a +b²) = (a +b), then <br> (a) 6V3 cm <br> Mathematics <br> 9. Simplify: <br> (6) V5 +V <br> 4. Euclid stated that all right angles are equal to each other in the form of <br> (b) a definition <br> (a) an axiom <br> 10. Factorise: 216x <br> 8. In APOR, if ZR = 22, then <br> (a) QR>PR <br> -2 <br> + <br> O VK GIlobal Publications Pvt. Ltd. <br> (b) ab = 0 <br> 1 <br> 6. The side of an isosceles right triangle of hypoteneuse 6/2 cm is <br> 125 <br> Section - A <br> (6) 6 cm <br> Question numbers 9 to 14 carry 2 marks each. <br> 3. (c) V5 -3 <br> (b) 372 cm? <br> (6) PQ =PR <br> (c) 0 <br> 2 <br> (c) only <br> (c) a postulate <br> (c)a= b <br> -1 <br> 7. The area of a parallelogram ABCD whose adjacent sides measure 34 cm and 20 cm and the diagonal <br> AC measures 42 cm is <br> (a) 336 cm? <br> (c) 8 cm <br> Section- B <br> (c) 420 cm? <br> (c) PQ<PR <br> Maximum Marks: 90 <br> (d) <br> V5-3 <br> (d) 6 <br> 16 <br> (d) a proof <br> (d) 2a = b <br> (d) 12 cm <br> (d) 672 cm? <br> (d) QR<PR <br>
196 <br> Mathematics IX: Term -I <br> 11. Determine the remainder when the polynonial p(*)=x - 3x+2* +1 is divided by x -1. <br> 12. The statements that are proved are called axioms. State whether the statement is true or false. Justify <br> your answer. <br> 13. Find the coordinates of a point which lies: <br> (0) below *-axis and on y-axis at a distance of 6 units. <br> (2) to the right of origin and on x-axis at a distance 6 units. <br> 14. In Fig. 1, if AB||CD, ZAPO = 50° and ZPRD = 127°, find x and y. <br> In Fig. 2, show that AB > AC. <br> 3 <br> 16. Simplify: /81 -8216+15/32+225. <br> Question numbers 15 to 24 carry 3 marks each. <br> 15. Locate /13 on the number line. <br> 5 <br> find the value ofk. <br> OR <br> x+2 <br> A <br> X, <br> P <br> OR <br> Fig. 1 <br> Fig. 3 <br> 17. Ifx =is a root of the polynomial f(x) = 6x-1lx+kx -20, find the value of k. <br> OR <br> 18. Using a suitable identify evaluate (104). <br> find the value ofx. <br> R <br> 1 <br> If the polynomials ky +4y +3y -4 and y-4y +*leavethe same remainder when divided by (y-), <br> Section - C <br> 2 <br> B <br> 127° <br> 20. In Fig. 4, if AB|| CD, find the value of x. <br> 19. In Fig. 3, we have BX =AB, BY = BC and AB = BC. Using Euclid's axiom, show that BX = BY. <br> B <br> 105° <br> Fig. 4 <br> D <br> 25° <br> 21. In Fig. 5, APLQR,PR> PQ and PS = PQ, Show that AR>A0. <br> 120° <br> E <br> P <br> Fig. 2 <br> 110° <br> Fig. 5 <br> R <br> VK GIobal Publications Pvt. Ltd. <br>
24. <br> randFare respectively the mid-points of equal sides AB and AC of AABC. Show that BF= CE. <br> 99. AD and|BC are equal perpendicular to a line segment AB. Show that CD bisects AB in Fig. 6. <br> 93. In Fig. 7, find the value ofx. <br> OR <br> -6 <br> 5+/6 <br> Ouestion numbers 25 to 34 carry 4 marks each. <br> 25. IF5-y <br> Ifa =3-2/2, find a" +g <br> 27. Factorise: <br> =a-b/6, find the values ofa and b. <br> OR <br> 64 <br> 125 <br> A <br> Fig. 6 <br> 96 <br> -a-8- a+ <br> 25 <br> Find the perimeter and area of a triangle whose sides are of lengths 52 cm, 56 cm and 60 cm <br> respectively. <br> 26. If,2 = 1.414 and /5 = 2.236, find the value of. <br> OR <br> Factorise: z+3z +3z-7. <br> BC = DE. <br> C <br> 48 <br> 5 <br> 29. Factorise: x+13x +32x +20. <br> Section - D1 <br> -a. <br> 28. Ifa+p=2, prove that +6ap + -8 =0. <br> Model Question Papers <br> 31. Prove that the angles opposite to equal sides of a triangle <br> 30. Plot the following points and check whether they are collinear or not: <br> (1, 1) (2, -3) (-1, -2) <br> 32. In Fig. 8, Z0Q> R, PS is the angle bisector of the ZQPR. PMLQR. <br> Prove that MPS =15°. <br> 35° <br> 33. A riangle ABC is right-angled at A. AL is drawn perpendicular to <br> BC. Prove that /BAL = ACB. <br> 2 <br> V10 -5 <br> up tothree places of decimal. <br> 2\/2 <br> are equal. <br> 34. In Fig. 9,AC = AE. AB = AD and BAD = EAC. Show that <br> 45° <br> E <br> B <br> Fig. 7 <br> iP. <br> G30 <br> 80 <br> M <br> S <br> Fig. 8 <br> 197 <br> Fig. 9 <br> s0°/ <br> R <br>
Time: 3 hours <br> General Instructions: As given in Model Question Paper (Unsolved). <br> 1. Every rational number is <br> Question numbers 1 to 8 carry l mark each. <br> (a) a whole number <br> (a) 0 <br> (a) 2 <br> Model Question Paper (Unsolved) -4 <br> Summative Assessment - l <br> 2. When the polynomial y +3y² +3y +1 is divided by y +l, the remainder is <br> (a) 0 <br> 3. The degree of the polynomial (* +9)(5-*2) is <br> (a) 84 cm2 <br> 4. The number of dimension a point has is <br> (a) 10 cm <br> (a) 0 <br> 2 <br> Mathematics <br> (6) a natural number <br> (6) 4 <br> 8. Angle x in Fig. 1. is <br> (a) 30° <br> (c) 40° <br> (b) 1 <br> 5. The area of a triangle whose sides are 13 cm, 14 cm and 15 cm is <br> (6) 1 <br> (i) a rational number <br> 10. Expand (4a -b+2c)*. <br> Section -A <br> (b) 168 cm² <br> (b) 20 cm <br> (6) 1 <br> (d) -1 <br> (c) a real number <br> 7. If+ =1, (a 0, b 0), then the value of a +b is <br> b <br> (b) 50° <br> (d) 60° <br> (c)–4 <br> 6. If the area of an equilateral triangle is 25/3 cm², then the perimeter of the triangle is <br> Question numbers 9 to 14 carry 2 marks each. <br> (c) 4 <br> (c) 2 <br> (c) 91 cm? <br> (c) 30 cm <br> B <br> Section - B <br> 9. Give an example of two irrational numbers whose product is <br> (ü) an irrational number <br> 45° <br> 105° <br> Maximnum Marks: 90 <br> Fig. 1 <br> (d) an integer eh <br> (d) 2 <br> (d) 0 <br> (d) 3 <br> (d) 105 cm? <br> (d) 40 cm <br> D <br>
11. Evaluate 105 X 106 using an identity. <br> 19. Write the coordinate of the point where x-axis and y-axis intersect. Also find the coordinate of a point <br> whose ordinate is -5 and which lies on y-axis. <br> 13. "For every line l and for every point pnot lying on a given line l, there exists a unique line m passing <br> through pand parallel to l" is known as Play fair's axiom. Is the above statement true or false? Justity <br> your answer. <br> 14. In triangles ABC and PQR, A = LP, B = LQ and AB =QR will <br> the two triangles be congruent? Give reasons for your answer. <br> 17. <br> In Fig. 2, AB and CD bisect each other at 0. Prove that AC= BD. <br> Ouestion numbers 15 to 24 carry 3 marks each. <br> 15. Express 0.0032 in the form of, where p and g are integers and q 0. <br> 16. Represent N93 on the number line. <br> OR <br> OR <br> 2 <br> If 3 =1732 and y2 = 1.414, then find <br> Section-C <br> Find the remainder when b(x) = 4x-12x +14x-3 is divided by <br> g«) =x <br> 18. Factorise: 8x +27y +36xy +541y². <br> OR <br> Simplify: (2x +p-)*- (2*- p+q) <br> Model Question Papers <br> values of a andb. <br> 19. In Fig. 3, we have ZABC = ZACB, Z3 = 24. Using an Euclid axiom, <br> show that 1=Z2. <br> 20. In Fig. 4, ifx +y = w +z, then prove that AOB is a line. <br> In Fig. 5, AD = AE and ZBAD= ZCAE. Prove that AABC is isosceles. <br> B <br> VK Global Publications Pvt. Ltd. <br> A <br> Fig. 5 <br> 21. S is any point in the interior of APQR. Show that SQ +SR < PQ +PR. i tott tnsti <br> 22. In Fig. 6, ZAOC and ZBOC form a linear pair. If a-b= 20°, find the <br> Fig. 2 <br> A <br> Fig. 3 <br> Fig. 6 <br> 199 <br> 3 <br> 2 <br> x <br> Fig. 4 <br> D <br> B <br>
200 <br> 23. In Fig. 7, AM and DN are the medians. Then tind <br> the value of DF. <br> Mathemotics IX: Term -I <br> 24. A rhombus shaped ficld has grass for 18 buffaloes to <br> 25. <br> ELe 8raze on. If each side of the rhombus is 30 m and its <br> longer diagonal is 48 m. how much area of the field <br> will cach buffalo <br> graze on, ifall the buffaloes on equal <br> arca. <br> Question numbers 25 to 34 carry 4 marks each. <br> find the value of 2%-7x-2x +1. <br> 29. <br> 30. <br> Ifx = <br> 26. Simplify the following expression: <br> (V3 +1)(1-/12)+ <br> 2+/3 <br> OR <br> 27. Factorise: r'+3r+3r-7 <br> Rationalise the denominator of the following: <br> 4V3 +52 <br> /3 +/12 <br> V48 +/18 <br> 28. Factorise: (*²-y)² +(y? -z2)+(z?-*2)2. <br> Section - D <br> OR <br> Factorise: x -7x-8. <br> 2 <br> (i)(-3, -5) <br> () (3, -5) <br> (iiü) (-4, 5) <br> Also, verify by locating them on the cartesian plane. <br> Write the quadrant in which each of the following points lie: <br> 32. In Fig. 8, bisectors of ZB and D of <br> quadrilateral ABCD meet CD and <br> 4 cm <br> AB <br> produced at P and Q respectively. Prove that <br> LP+ LQ-(LABC+ LADC). <br> A <br> Without actualdivision, prove that 2x –5x +2*-x+2 is divisible by x-3x +2. <br> B <br> 23. IfD is the mid-point of the hypotenuse AC of a <br> right-angle triangle ABC, then prove that P <br> BD =AC. <br> 6 cm <br> M <br> 4S cm <br> (iv) (3, 4) <br> 31. Prove that two triangles are congruent if two angles and the included side of one triangle are equal to <br> two angles and the included side of other triangle. <br> D <br> C <br> Fig. 7 <br> Flg. 8 <br> E <br> B <br> 34. If the altitudes from the vertices of a triangle to the opposite sides are equal, then prove that the <br> triangle is isosceles. <br> VK Global Publications Pvt. Lta. <br>
Time: 3 hours <br> Ceneral nstructions: As given in Model Question Paper (Unsolved) 1. <br> (a) 3 <br> Question numbers I to 8 carry l mark each. <br> 1. Value of (8 1) x (81)0.09 is equal to <br> (a) -5 <br> (a) 1 <br> 2. The degree of the polynomial (*+5)(4 -*) is <br> (a) 0 <br> Model Question Paper (Unsolved) -5 <br> Summative Assessment - <br> (a) remains the same <br> (a) 100 m <br> g Jf(: +1) is a factor of the polynomial x- +k, then the value ofk is <br> 4. The number of dimensions, a solid has is <br> a+b is <br> (b) 9 <br> (a) -7 <br> Mathematics <br> 5. If the sides of a triangle are trebled, then its area <br> (c) 14 <br> (b) 2 <br> (a) 80° <br> (6) 0 <br> (c) 60° <br> (b) 1 <br> Section -A <br> OVK Global Publications Pvt Ltd. <br> (6) becomes two times <br> (b) 160 m <br> (b) 7 <br> (d) 8 <br> (6) 70° <br> (a) 50° <br> (c) 27 <br> 6. The sides of a triangle are in the ratio 16: 18:25 and its perimeter is 590 m. The smallest side of the <br> triangle is <br> Question numbers 9 to 14 carry 2 marks each. <br> (C) 3.: <br> 9. Find two rational numbers between -l and <br> (c) 2 <br> (c) 2 <br> 2 <br> 0 <br> 7. If (* +2)'and (x -2) are factors of ax +2*-3x+ bx -4, then the value of <br> (c) becomes three times <br> (c) 180 m <br> Section -B <br> Maximum Marks: 90 <br> 8. In Fig. 1, BO, CO are the bisectors of external angles CBE and ZBCD <br> respectively of A ABC. Then ZBOC is equal to <br> (d) 81.25 <br> 10. Find the value of5 +7+(-12) without calculating the cubes. <br> (d) <br> (d) -2 <br> (d) 3 <br> (d) becomes nine times <br> (d) 250 m <br> i B <br> i <br> A <br> Fig. 1 <br>
202 <br> Mathematics IX: Term -1 <br> 11. Expand: (3a-5b-c)'. <br> 12. Which of the following points. do,not 1he on w 9zest Where d thhef e <br> A(-2, 3), B(0, -4), C(5, 0), LD(-3, -5) <br> 13. In Fig. 2, find the value of for which the lines I and m are <br> In Fig. 3, if AB ||CD, Z1 : 24 = 3:2, then fínd 6. <br> 14. The edges of a surface are curves. State whether the statement ís true or false, Justity yor T5me <br> OR <br> and b <br> OR <br> Question numnbers 15 to 24 carry 3 marks each. <br> Locate V17 on the number line. <br> 2-V5 <br> 16. Ifa = <br> 2+/5 <br> 15. Express the decimal number 2.218 in the forn of,q0. <br> 2+V5 <br> 2-F <br> 17. Factorise: 2x +3/5x +5. <br> Flg, 2 <br> OR <br> 445 <br> find a?-52 <br> 18. Evaluate (103) by using an identity. <br> Section -C <br> Factorise: 16x+4y+9z-16xy-12yz + 24L. <br> 20. In Fig. 4, AB || CD, Determine x. <br> OR <br> 19. It is known that x +y =10 and that x = z. Show that z +y = 10. <br> Solve the question usíng appropriate Euclid's axiorm. <br> 21. Prove that the bisectors of angles of a linear pair are at right angles. <br> D <br> 4cm <br> AABC and ADBC are two isosceles tríangles on the sarme base BC. Show that ZABD=ACD. <br> 22. In Fig. 5, if line l is the bisector of LA, then find 02 <br> Fg. 5 <br> Fia, 4 <br> VK Globat Publications Pn L0 <br>
23. In AABC, (Fig. 6), 4AB = AC and AD is angle bisector of ZA. <br> Prove AABD AACD. <br> 24. A perimeter of a triangle is 420 metres and its sides are in the ratio of 6:7:8. <br> ad the area of the triangie. <br> Question numbers 25 to 34 carry 4 marks each. <br> 25. Factorise: (2a +3b)* -(2a-36)'. <br> Factorise: a'-!12 <br> 26. Show that: alb-c) <br> 5+3/3 <br> 27. Ir <br> 7+4/3 <br> OR <br> =1 <br> =a+b3, find the values of a andb. <br> OR <br> Simplify by rationalising the denominator <br> 2/6 6/2 843 <br> 2+V3 +V3 6 +2 <br> 4Section 1-DTOR <br> 98. If the polynomials az +3z* -13 and 22 -5z +a leave the same <br> remainder when divided by z +2, find the value of a. <br> 29. Find the value of -86° -36ab -216, when a = 2b +6. <br> s <br> 30. If two lines intersect each other, then prove that vertically <br> opposite angles are equal. <br> 31. Prove that the sum of any two sides of a triangle is greater than <br> twice the median drawn to the third side. <br> 32. In Fig. 7, LM is a line parallel to the y-axis at a distance of3 units. <br> () What are the coordinates of the points P, R and Q? <br> (ä) What is the difference between the abscissa of the points L and M? <br> (i) Name the point equidistant from the point R. <br> A <br> E <br> Model Question Papers <br> Fig. 8 <br> B <br> D <br> Fig. 7 <br> 33. AD, BE and CF, the altitudes of triangle ABC are equal. Prove that triangle ABC is an equilateral triangle. <br> 34. In Fig. 8, AB is a line segment and P is its mid-point. D and E are points on the same side ofAB such <br> that ZBAD=ABE and EPA= 2DPB. Sh0w that AD = BE. <br> Fig. 6 <br> OM <br> 203 <br>
Time: 3 hours <br> General Instructions: As given in Model Question Paper (Unsolvea) <br> (a) equal <br> (c) unequal <br> Question numbers 1 to 8 carryl mark each. <br> 1. The things which are double of same thing are <br> (a) -2 <br> 2. If (x-2) is a factor of 2x-6x +5x +c, then c is <br> 3. The number (3 -1l)(3+V11) is <br> (a) a natural number <br> Model Question Paper (Unsolved) -6 <br> Summative Assessment - ! <br> (c) a rational number <br> 10. <br> (a) 2 <br> (a) <br> 4. The degree of the polynomial 2- y* -y° +2y' is <br> 240 <br> Mathematics <br> (a) 26 <br> (6) 2 <br> (6) 7 <br> (a) QP=5 cm, ZP= 60° <br> (c) QR =5 cm, R= 80° <br> Section -A <br> 7. Ifa+b=-1, then the value of a +b -Bab is <br> Expand <br> (b) 525 <br> 5. Arhombus sheet whose perimeter is 40 m and one diagonal is 12 m long is painted on both sides at the <br> rate of5 m². The cost of painting is <br> (6) 3/3 cm² <br> (6) 1 <br> 6. The altitude of an equilateral triangle is 3/3 cm. The area isisletr <br> (a) 6/3 cm² <br> (6) halves of same thing <br> Question numbers 9 to 14 carry 2 marks each. <br> 9. Simplify /81 -8/216 +15/32 +/225. <br> (d) double of the same thing <br> (c) 18 <br> (6) a whole number <br> (d) an irrational number <br> (c) 0 <br> (c)480tle <br> Maxinum Marks: 90 <br> (c) -1:st <br> 8. Triangles ABC and PQR are congruent. If AB - 5 cm, ZB= 40° and ZA= 80°, then which of the <br> following is true? <br> (d) -18 <br> (6) QP = 5 cm, ZR = 60° <br> (d) QR =5 cm, ZQ= 40° <br> Section - B <br> (d) 3.ih <br> (c) 12V3 cm² i e (d) 9/3 cm² ( <br> (d) 960 <br> (d) -26 <br> VK Global Publications Pvt. Ltd. <br>
11. Determine whether (3x -2) is a factor of 3: 3 <br> figure so formed and write its one property. <br> 13. In Fig. 1, ifx =61° and y =118°. Is ml|n? <br> 12. Plot the points A (3, 0), B (3, 3) andC(0,3) in a Cartesian plane. Join OA, AB, BC and CO, Name the <br> m <br> Fig. 1 <br> 4 In Eig.2, AC = XD, C is mid-point ofAB and D is mid-point of XY. Using Euclid's <br> axiom, show that AB = XY. <br> Ouestion numbers 15 to 24 carry 3 marks each. <br> b (ü)O is also the mid-point of BC. <br> 1 <br> „2 <br> Lines PQ and RS intersect each other at point 0. If ZPOR: ZROO =5: 7 find all the remaining angles. <br> 15. E and F are respectively the mid-points of equal sides AB and AC of AABC. Show <br> that BF= CE. <br> OR <br> Factorise: 6x +5x -6 <br> In Fig. 3, ine segment AB||CD and O is the mid-point of AD. Show that <br> (i) AAOB ADOC. <br> 17. Factorise: x*++2-2x -–, <br> +x*-20x +12. <br> OR <br> 16. Express 0.001 in the form of , where p and q are integers and q # 0. <br> OR <br> 19. Simplify : (a +b+c)* -(a-b-c)*. <br> Model Question Papers <br> Section-C <br> 20. Locate /5 on the number line. <br> VK GIobal Putblications Pvt. Ltd. <br> OR <br> 18. Find the area of a triangular park whose sides are of lengths 120 m, 80 m and 50 m. <br> Prove that /5 -3 is not a rational number. <br> Z1. In Fig. 4, AB||CD. CD||EF and y :z = 3:7, find the measure of x, <br> yC <br> and z. <br> B <br> A <br> Fig. 2 <br> 205 <br> Flg. 4 <br> Flg. 3 <br> B <br>
206 <br> 22. <br> Mathematics IX : Term -I <br> Show that the angles of an equilateral triangle are 60° eacl <br> 23. Iltwo interior angles on the same side ofa transyersal intersecting two parallel lines are in the:ratio 2:3, <br> then find the larger of two angles. <br> ng D, ioP | RS, ZOPQ= |10° and 2ORS = 130°, then determine ZPQR. <br> + <br> P <br> 110° <br> Question numbers 25 to 34 carry 4 marks cach. <br> 25. Evaluate: <br> +... + <br> /2 +1 N3 +2 4+3 <br> Flg. 5 <br> OR <br> Ifx =2+/3, find the value ofx+. <br> Factorise: x -64 <br> OR <br> Section-D <br> 26. Simnplify the following by rationalising the denominator: <br> /9 +8 <br> R <br> 130° <br> 27. Ifthe polynomials ax +4x+3x 4 and x-4x +aleave the same remainder when divided by (x -3). <br> find the value ofa. <br> 28. In Fig. 6, AC = BC,ZDCA = ZECB and ZDBC = ZEAC. Prove that (i) ADBC AEAC(ii) DC = EC and <br> BD = AE. <br> AC <br> 29. Ifa +b +C=9 and ab +bc + ca = 40.finda'+2 +. <br> Flg. 6 <br> S <br> 6–4/3 <br> 6+4/3 <br> Di. Esis E <br> © VK Global Publications Pvt. Lt. <br>
From the Fig. 7, write <br> 5 <br> B <br> (0) the coordinates of the points B and E. <br> (m) the abscissa of the points D and H. <br> (v) the quadrant in which points B and I lie. <br> (ui) the perpendicular distance of the point G from the x-axis. <br> (uin) the perpendicular distance of the point I from the y-axis. <br> Fig.7 <br> <QTR1 <br> (vii) the point whose perpendicular distance from y-axis is 2 units. <br> 31. Prove that the sum of the angles of a triangle is 180°, <br> 2 <br> JZ. D is a point on side BC of AABC such that AD = AC. Show that <br> AB > AD. <br> in ig. 8, the side QR of APOR is produced to a point S. Ifthe bisectors <br> of PQR and <br> meet at point T, then prove that <br> QPR. <br> Model Question Papers <br> (i) the point identified by the coordinates (1, 1). <br> (iv) the ordinates of the points A and C. <br> PRS <br> VK Global Publications P Ltd. <br> Q <br> P <br> 207 <br> Ri <br> Fig. 8 <br> 34. Without actual division, prove that (2x -6x+3+3r -2) is exactly divisible by (r*-3r +2). <br>
Time: 3 hours <br> General Instructions: As given in Model Question Paper (Unsolved): <br> Model Question Paper (Unsoived) -? <br> Summative Assessmert - I <br> (a) 1 <br> Question numbers 1 to 8 carry l mark each. <br> 1. Ifx +kx +6 = (* +2)(x +3) for all x, the value ofk is <br> Mathematics <br> (b) 1 <br> (c) 0.101001000100001... <br> (a) 60 cm <br> 2. Which of the following is a rational number? <br> (a) V5 <br> (b) 48 cm <br> 5. If*+=62, then + <br> (6) 3415 <br> 3. The lengths of the sides of a triangle are in the ratio 3 :4:5 and its perimeter is 144 cm. The height of <br> the triangle corresponding to the longest side is <br> (c) a right triangle <br> Section -A <br> (a) 512it el tl () 488 <br> equals <br> (a) an acute angled triangle <br> (6) p(-b la) <br> 4. An isOsceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Its area is <br> (a) 9/15 <br> (c) 5 <br> (b) Tt <br> (d) 0.853853853... <br> (a) A line segment has definite length <br> 6. When p(¢) is divided by ax -b, then the remainder is <br> (a) pla + b) <br> (c) 28.8 cm <br> (c) 9V14 <br> 7. The angles of a triangle are in the ratio 5:3:7. The triangle is <br> Question numbers 9 to 14 carry 2 marks each. <br> 9. Evaluate: (343)-2 <br> (c) pla/b)iixs <br> (c) 504 ios 2sh (d) 498 <br> 8. Which of the following statements is incorrect?. <br> (d) an isosceles triangle <br> (6) Three lines are concurrent if and only if they have a common point <br> Maximum Marks: 90 <br> (d) 3 <br> (b) obtuse angled triangle <br> (c) Two lines drawn in a plane always intersect at a point. <br> Section - B <br> (d) 36 cm <br> (d) 9V13 <br> (d) pbla) <br> (d) One and only one line can be drawn passing through a given point and parallel to a given line. <br> OVK Global Publications Pvt LIO. <br>
10. Factorise: 7/2x-10x -4 <br> 1 <br> Ifa+b+c=7and ab +bc + ca= 20, find the value of 2 +)'+c. <br> 19 In Fig. 1, if AB||CD, then find the value of x. <br> 1 <br> (i) Coordinates of point A <br> (2) Abscissa of point D <br> fF <br> 13. In Fig. 2, ZPQR=PRQ, then prove that ZPQS = ZPRT. <br> Q/2r- 10° <br> OR <br> 14. See Fig. 4, and write the following: <br> L <br> P <br> Fig. 1 <br> VK Global Publications Pvt. Ltd. <br> In Fig. 3, sides QP and RQ of APQR are produccd to point S and T <br> respectively. If ZSPR=135° and ZPQT =110°,find ZPRQ, <br> OR <br> Locate W4.7 on the number line. <br> 5x-20° <br> -2 <br> -3 <br> -1t <br> -5 <br> y <br> +4 <br> 5 <br> +3 <br> -4+ <br> F2 <br> B <br> Fig. 4 <br> (ii0) The point identified by the coordinates (5, 4) <br> (iv) Coordinates of point C. <br> Question numbers 15 to 24 carry 3 markS each. <br> 15. Represent /5 on the number line. <br> 1. 2 34 <br> 345 6 7, X <br> B:6 <br> Section -C <br> Model Question Papers <br> S <br> T <br> 110° <br> Fig. 2 <br> Fig. 3 <br> R <br> 209 <br> 4S <br> T <br> I35" <br> R <br>
210 <br> 16. Express 5.347in the form 2 where and a are integers arnd g #U <br> Mothematics IX :Term -| <br> 17. Factorise: 2J243 <br> 18. <br> +863 <br> -27c +18/2abc. <br> OR <br> 23. <br> Factorise: (ax + y) +(ay - bx), <br> rIg 2, D 1s a point on side BC of AABC Such that AD = AC. Show te <br> AB> AD. <br> 1S. In ig. 6, ZX =72°,ZXZY 46°.IfyO andZ0 are bisectors of XYZ and zz <br> respectively of AXYZ, find Z0YZ and ZYOZ. <br> OR <br> 72 <br> Fig. 6 <br> In Fig. 7, AD = CE are the angle bisectors of ZA and ZC respectively. If <br> ZABC =90°, then findZAOC. <br> 20. Find the value of 64x +1252, if4x +5z= 19 and xz = 5. <br> A <br> 21. In AABC, BE and CF are altitudes on the sides AC and AB respectively such that BE = CF. Using RHS <br> congruency rule, prove that AB = AC. <br> In Fig. 8, OD is the bisector of ZAOC. OE is the bisector of ZBOC and OD LOE. <br> Show that the points A, and B are collinear. <br> 22. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are <br> 15 cm, 14 cm and 13 cm and the parallelogram stands on the base l5 cm, find the height of <br> parallelogram. <br> c <br> Fig. 8 <br> V5 +/3 V3 +/2 V5 +V2 <br> 26. Ifa=7-443, find the value of va + <br> 24. In Fig. 9, if AC is the bisector of ZA and 2C and A= 3, show that ZA= LC. <br> Question numbers 25 to 34 carry 4 marks each. <br> 2 <br> 25. Simplify: <br> B <br> Va <br> Fig. 5 <br> Section - D <br> D <br> Fig. 7 <br> C <br> Fig. 9 <br> VKGlobal Publications Pt. Ltd. <br>
27. <br> Find the values of a and b ir7+345 :7-3/5 Ci <br> 3+V5 3-5 <br> OR <br> Which of the following points lie on the negative side ofx-axis? Which of them lie on the posiive side of <br> y-axis? <br> (-2, -2), (-4,0), (-3,2), (0, -4), (5,-7), (1,3), (-6,-5)(3, -2) <br> Which of the above points do not lie in any of the quadrants? <br> 29. Simplify) <br> 98. The polynomial () =**-2%° +3x - ax +3a-7 when divided by (x +1) leaves the remainder 19. <br> Find the value of a. Also find the remainder, when b(x) is divided by x +2. <br> =04: <br> Find the values of a and b so that (* +1) and (* -1) are factors ofx +ax-3x+2x +h. <br> 3 <br> OR <br> 20 Prove "If twolines intersect each other, then the vertically opposite angles are cqual". <br> that AB = AC. <br> (ü) Factorise: a + b–2(ab- ac +bc). <br> 31. In Fig. 10, the sides AB and AC of AABC are produced to points E and D respectively. If bisectors BO <br> and CO of ZCBE and ZBCD respectively meet at point O, then prove that BOC=90°BAG. <br> © VK Glebal Publications Pvt. Ltd. <br> B <br> Model Question Papers <br> A <br> 32. () Muliply 9x* +25y* +15xy +12x -20y +16 by 3x -5y -4 using suitable identity. <br> Fig. 10. <br> D <br> C <br> 211 <br> 33. In Fig, 1I,D and E are points on the base BC of a AABCsuch that 4D = AE and ZBAD = ZCAE. Prove <br> Flg. 11 <br> 2 <br> 34. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD, show that ZA> LC <br> and ZB> ZD. <br>
Time:3 hours <br> General Instructions: As given in Model Ouestion Paper (Unsolved)-1: <br> 1. The number (2 -/6)(2 +V6) is <br> is <br> Question numbers 1 to 8 carry l mark each. <br> (a) 9 <br> (a) a natural number (6) a whole numberso t(c) a rational number <br> (a) first axiom <br> 2. The numerical coefficient of y in (3x -) isg i: <br> 4. x +is <br> MOdel Question Paper (Unsolved) -8ha <br> Summative Assessnent - <br> (a) a polynomial of degree 1 <br> (c) a polynomial of degree 0 <br> (a) 1 <br> (a) 54/3 cm² <br> 3. It is known that ifx +y =l0,then x +y +z=10 +z. TheEuclid's axiom that illustrates this statemment is <br> (b) second axiom <br> Mathematics <br> of the triangle is <br> (a)27 cm? <br> (c) 54/7 cm² <br> (6)– 27 <br> () a+c +e=1 80° <br> (a) only (Ö) <br> bi (6)- 1 <br> (c) only (üi) <br> 5. Which of the following numbers is not a zero of the polynomial 2x * +9x +llx + 4x -6? <br> 6. The height of an equilateral triangle measures 9 cm. Its area is <br> Section -A <br> (ii) <br> iheant <br> (6) 144/3 cm? <br> (b) 27/7 cm² <br> (d) 54 cm? <br> (c) -1 <br> b +f = c+e <br> (b) only (ü) <br> (c) third axiom <br> 7. The perimeter of an isosceles triangle is 42 cm and its base is times each of the equal sides. The area <br> 8. In Fig. 1, which of the following statements must be true? <br> (c) -3 <br> (d) both (i) and (ü) <br> (6) a polynomial of degree 2 <br> (d) not a polynomial <br> (c) 27/3 cm² <br> Maximum Marks: 90 <br> (d) an irrational number <br> (i2) a +b=d +c <br> (d) - 9 <br> Fig. 1 <br> (d) fourth axiomn <br> (d) 3 <br> (d) 108 cm? <br>
Question numbers 9 to 14 carry 2 markS each. <br> 10. <br> o Find two irrational numbers betweenand <br> 11. Expand <br> Find the value of a if (x -a) is a factor of x-a'x +x +2. <br> 2 <br> 8 si sSection B <br> 16. Ifa = <br> 12. Are there any points in the cartesian plane which do not belong lo any <br> quadrants? If so, name such points. <br> 2+/5 <br> 2-/5 <br> 15. Locate /4.5 on the number line. <br> Simplify: <br> 13, In Fig. 2, the sides BC,CA and AB ofa ABC have been produced to D. E andr <br> respectively. If ZACD = 105° and EAF = 45°, find all the angles of AABC. <br> Question numbers 15 to 24 carry 3 marks each. <br> and b <br> If the supplement of an angle is four times its complement, find the ngle. <br> 14. In ADEF, D =70° and E =30°, which side of this triangle is the longest? <br> 2V6 <br> 2-45 <br> 2+/5 <br> 17. Factorise: 2x +432*y <br> OR <br> 642 <br> B <br> Factorise: 8(x + y)-27(x - y) <br> © VK Global Publications Pvt. Ltd. <br> 2 <br> OR <br> 3 <br> then find the value ofa' -b. <br> 8/3 <br> OR <br> 18. Evaluate 108 using a suitable identity. <br> 4 <br> 135° <br> Section -C <br> Fig. 3 <br> OR <br> Model GQuestion Papers <br> of' the <br> In Fig. 4, if l, || l, and 1||l4, find y in terins of a. <br> E <br> 45/ <br> 19. If a point lies between two points P and R such that PQ =QR, then prove that PQ =-PR. <br> Fig. 2 <br> ) <br> 2 <br> 20. In Fig. 3, if the bisectors of base angles ofa triangle enclose an angle of 135, prove that the riangle is ia <br> right triangle. <br> 105° <br> Fig. 4 <br> 213 <br> D <br>
214 <br> 21. If the bisector of the exterior vertical angle of a triangle is parallel to the base, show that the trianglei <br> Z3. <br> Mathematics X : Term -1 <br> 22. In Fig. 5, If AB||CD||EF, PQI|RS, . <br> Z4. <br> isosceles. <br> 26. <br> A <br> 25. Simplity: <br> (25)2 x (243)5 <br> 70\/Q <br> O Is alny point in the interior ofAABG. Prove that AB +BC +CA>0A +0B +0C. <br> (L6)4 x (8)3 <br> Find the value of. <br> Ihe lengtlh of the sides ofa triangle are in the ratio of3 :4:5 and itsperimeter is 144 Cn. Find the area <br> of the triangle. Also, find the height corresponding to its longest side. <br> Question nunbers 25 to 34 carry 4 marks each. <br> OR <br> Ifx =3+8,find the value ofx+ <br> 29. Factorise: )" + pg <br> 30° <br> 4 <br> Fig. 5 <br> /3-/2-l <br> 4 <br> OR <br> ZRQD =30° and ZCQP <br> R <br> B <br> 27. If() =**-58 +7, evaluate f2)– f-) +f <br> Section - D <br> 28. IfVm +u-p=0, then find the value of (m +n - p)² <br> +1+2þ+9 <br> Correct to the three places of decimal if 2 = 1.414 and /6 =2.45 <br> = 70°, then find QRS. <br> Factorise: (2a-36) +(36–4c) +(4c- 2a) <br> 30. In Fig. 6, PTLQR and PS is the bisector of ZP. I! <br> 20=60° and ZR=30°, findZTPS. <br> 60° <br> Fig. 6 <br> 30 <br> R <br> ©VKGlobal Publications Pvt. Ld <br>
B <br> 31. In Fig. 7, Side BC of a AABC is produced to a noint n The bisector of ZA meets BC at L rove <br> LABC +ACD =2/ALC <br> Fig. 7 <br> 32. In Fig. 8, PORS is a quadrilateral where PQ = RO, ZPQT= ZRQU, <br> LTOS = ZUQS. Prove that QT =QU. <br> B <br> Model Question Papers <br> 33. In an isosceles triangle ABC (Fig. 9), AB AC. bisectors of ZB and 2C <br> intersect each other at 0. Show that (i) OB = OC (ü) AO bisects ZA. <br> A <br> Fig. 9 <br> R <br> U <br> 215 <br> Fig. 8 <br> 34. On plotting the points A(1,0), B(5, 0), C(5, 4) and D(1, 4) and joining AB, BC, CD and DA, which tigure <br> is obtained? Find its area. <br>
Time: 3 hours <br> General lhustructions: As given in Model Queslion Paper (Unsolved) a <br> 2. <br> Question uumbers 1 to 8 carry l mark each. <br> 1. A rarional nunber between /2 and V3 is <br> 5. <br> 6. <br> (a) <br> 8. <br> (a) -2 <br> 3. V7 is a polyuomial of degree <br> Model Question Paper (Unsolved) - <br> Summative Assessnent - <br> 9. <br> (a) ) <br> The value of polynomial 3x-5x +2 al x =is <br> 4. Which of the following needs a proof? <br> (b) Definition <br> u) Axiom <br> (6) I.52 <br> The area of a rhombus <br> (u) 384 m <br> Mathematics <br> (6) <br> (u) x ++x+x +1 <br> IL is given thatAABG <br> Lrue? <br> (6) I <br> Section -A <br> 7. Which of the lollowing polynomials has (x +I) asa factor? <br> (C) DE=t.6 cm, Z=70° <br> (u) DE = 4.6 cm, Z) = 70° <br> (c) 1.92 <br> (0) x +x*+x +1 <br> (c) <br> (c) 7 <br> The area of a triaugle whose sides are 35 cm, 45 cm and 50 cnn is <br> (u) 75,6 cm² <br> (6) 75/13 cm² <br> (c) 25/13 cm² <br> whose perimeter is 80 m and one of whose cliagonal is 24 m is <br> (b) 192 <br> (c) 960 n' <br> (d) 520 <br> Questivn numbers 9 to 14 carry 2 marks cach. <br> Fil two irrational ounbers whosc sum is <br> (1) a rational number <br> (c) Theorem <br> Maximum Marks: 90 <br> Section - B <br> (ed) <br> (c) x+2x-2x +1 (d) x +3+3x +x +l <br> ADEF and AB =4.6 cm, ZB = 60°and ZA =50°.Then wlhich ofthe followiug is <br> (d) 1 <br> (iü) an irrativnal nunber <br> 2 <br> (d) Postulate <br> (b) DE =4.6 cIn, ZF =70° <br> (d) DF =4.6 Cm, Z = 60° <br> (ed) 150/26 cm² <br> VK Global Publications Pvt Lio <br>
10. <br> Factorise: 492 <br> 11. Give possible expressions for the length and breadth of the rectangle <br> whose area is a2 <br> 14. <br> 4 <br> -3a +2. <br> answer. <br> 12. If one of C the angles formed by two intersecting lines is a right angle,i4y <br> what can you say about the other three angles? Give reason for your <br> Find x andy il 7,||2, in Fig. 1. <br> 13. In Fig. 2, find ZDAC. <br> 120° <br> A <br> + <br> OR <br> 3/3 -2/2 343 +2/2 <br> Ouestion numbers 15 to 24 carry 3 marks each. <br> 3 <br> 15. Simplify: <br> 16. Express 23.43 in the form <br> D <br> OR <br> Fig. 2 <br> Ifx =3+2/2, find the value of Vx - <br> The base BC of an equilateral riangle ABC with side BC = 8 units lie along x-axis such that the <br> mid-point of the base is at origin. Find coordinatesofB and C. Also find coordinates of third vertex A, <br> ifA lies along positive direction ofy-axis. <br> © VK Global Publicatons Pvt. Ltd. <br> 20° <br> OR <br> Model Guestion Papers <br> Section -C <br> 17. If3x -7y = 10 and xy =-1, find the value of 9x + 49y* <br> Find the value of 4x+y²+252 +4xy -10yz -20zx, using the identity if <br> X =4.y =3,z=2. <br> 18. Find the value of1009' using a suitable identity. <br> 19. In ABC,ADL BC and AE bisects ZA. If ZB =45° aud ZC = 25°, tlhen fiud <br> ZDAE <br> (+ 2y): <br> 20. In Fig. 3,ZABC =80°,ZEFG = 45°:and ZEGF =35°. P'rove tat 1B|| DE. <br> 21. Arav and Kaay bave the sane height. If their heights increase by5 cm <br> cach, how will their new heights be compared: <br> 108° <br> Fig.1 <br> 217 <br> 35° <br> Fig. 3 <br> 45° <br> 80 <br>
218 <br> Mathematics IX : Tem -I <br> *etnat the length of the peTDendicnlars drnwn from vertices ofequal angiesN <br> of an isOSceles riangle to the opposite sides are cqual. <br> In Fig. 4, 4 Aand OE = OF, Prove that OC = 0B. <br> 23. In Fig. 5,ACLCE and ZA: ZB:2C=5:3:2, Find ZEGD. <br> 1 <br> 26. Ifyz =l, show that <br> 27. Simplify: <br> ** O adjacent sides ofa parallelogramare 5 cm and 3.5 cm, One ofits diagonals is 6.5 cm. l'ind the are <br> of the parallelogam. <br> Question numnbers 25 to 34 carry 4 marks each. <br> 25. If: + =119,find <br> Simplify: <br> -$ <br> ge-OR <br> 2187 7 <br> 956 4 <br> Factorise: x -64. <br> A <br> + <br> 1 +*+y l++z <br> A <br> OR <br> Fig. 5 <br> (1331) 3 <br> OR <br> 2 <br> 1 <br> Section - D <br> 29. Using factor theorenm, factorise the polynomialx°+x*-4x-4. <br> S <br> 28. Ifx+ax* + bx +6 has (x -2) as factor and leaves remainder 3 when divided by (x-3), fumd the valucs of <br> a andb. <br> Fig. 6 <br> 1 <br> I+2+! <br> 30. Prove that if two lines intersect cach other, then the vertically opposite angles are equal. <br> 31. In Fig. 6, APl and PR> PQ. Show that AR> AQ. <br> =1. <br> C <br> 3 <br> R <br> Flg. 4 <br> VKGlobal Publications Pvt. LU <br>
32. In Fig. 7, , the side QRof APQR is produced to point S. If the bisector of ZPQR and ZPRS meet at point <br> T. then prove that ZQTR=0 <br> R <br> VK Global Publications Pvt. Ltd. <br> Fig.7 <br> 33, Plot the following points and check whether they are collinear or not: <br> (6, -2), (1, 3), (–2, -4), (-l, 5) A- NoUDs <br> D, <br> 94. In Fig. 8, ABCD is a square. M is the nid-point of AB and PQ LCM. Prove that CP =CQ <br> Model Question Papers <br> M <br> Fig. 8 <br> 3 <br> 219 <br> -(0) <br>
Time: 3 hours <br> General Instructions: As given in Model Question Paper (Unsolved) <br> 1. <br> Question numbers 1 to 8 carry l mark each. <br> 243 <br> 32 <br> (a) <br> 32 <br> 243 <br> 8. <br> (a) 15 <br> 4 <br> Model Question Paper (Unsolved) -10 <br> Summative Assessmnent - <br> (a) 125 <br> is equal to <br> 2. If p(r) =**+2/2x-1, then p(2/2) is equal to <br> (b) -1 <br> 3. One of the factor of (25x -l) +(1 +5x) is <br> (a)5 +x <br> (6) 5 -x <br> 4. The coefficient of y in the expansion of (5-y) is <br> (6) <br> 5. Boundaries of surfaces are <br> (a) points <br> Mathematics <br> (c) l14 cm² <br> 6. In AXYZ, if XY < XZ, then <br> (a) X Y <br> (6)– 1 <br> (a) bya'b2 <br> (c) by2a-62 <br> (b) lines <br> 7. In Fig. 1, the area of quadrilateral ABCDis <br> (a) 102 cm? <br> (6) LZ< Y <br> Section - A <br> (b) 57 cm² <br> (d) 95 cm' <br> (b) 2%/a-b2 <br> (d) bya?262 <br> (c) <br> 16 <br> Question numbers 9 to 14 carry 2 marks each. <br> 81 <br> (c) 0 <br> The area of an isosceles triangle, the mcasure of one ofwhose cqual sides is <br> a units and third side is 2b units is <br> (c) 5x –1 <br> (c)– 75 <br> (c) curves <br> (c) ZY < L <br> Section -B <br> Maximnum Marks: 90 <br> (4) <br> 81 <br> 16 <br> (d) 7 <br> (d) 10x <br> (d) 15 <br> (d) surfaces <br> (d) ZY X <br> 17 cm <br> 15 cm <br> Fig. 1 <br> 9 cm <br> 12 cm <br> 9 There is a Dumber x such that x is irraLional bul x is rational. Is the statement true? Iustify your <br> answer by an example. <br> ©VK Global Publications Pyt. Ltd. <br>
10. Check whether b(*)=x-x+l is a mnultiple of g(x) =2-x or not.os fue 1tcti2 st <br> 11. For what value oft, 2x -3 is a factor of2x-9* + px +12. <br> 12. In which quadrant or on which axis each of the following points lie? <br> (-5,7), (6, 0), (-1, -1), (8, -5) <br> 13. In the given Fig. 2, 'a' is greater than 5' by one-sixth of a straignt angees a as/ <br> Find the value of a and b. <br> 14. Atransversal intersects two lines in such a way that the two interior <br> angles on the same side of the transversal are equal. Will the two lines <br> always be parallel? Justify your answer. <br> 15. Express 0.3178in the form <br> Question numbers 15 to 24 carry 3 marks each. <br> ls it possible to construct a trianigle with lengths of its sides as 10 cm, 9 cm and 4 cm? Give reason for <br> your answer. <br> Find the values of a and b if <br> 18. If? <br> of <br> 16. Ifa=5+2/6 and b =, then what will be the value of a' +62? <br> Factorise: 27x-y-1-9xy <br> OR <br> 4 <br> 1 <br> 17. Factorise: 25x+16y +4z"-40x) +16yz -20:xz <br> OR <br> +=62, find the value of x 3 <br> A <br> 3-/5 <br> D <br> = av5 <br> 3+2/511 <br> Model Question Papers <br> 4 <br> Section -C <br> Fig. 3 <br> 19. Solve the equationx +8 = 1l and state which axiom do you use here. ii <br> 20. In Fig. 3, we have ZABC=ZACB and Z3 = 24. Show that 1= /). <br> 2 <br> b <br> + <br> 3 <br> Fig. 2 <br> 21. AP and BQ are the bisectors of two alternate interior angles formed <br> by the intersection of a transversal n with lines l and n (see Fig. 4). If <br> AP||BQ, show that l||m. <br> 221 <br> A <br> Fig. 4 <br>
222 <br> Mathematics |X : Term -| <br> 22. Show that the sum of the three altitudes ofa t <br> Ln quadrilateral ABCD, AB is the longest and CD is the shortest side. <br> Prove that ZC>ZA and ZD> B. <br> OR <br> 23. In Fig. 5, if Z =Zy and AB = CB,prove that AE =CD. <br> 24. Find the cost of levelling a ground in the form ofa triangle having te <br> sides 51 m, 37m and 20 m at the rate of {3 per m". <br> Section - D <br> Question numbers 25 to 34 carry 4 marks each. <br> 25. Prove that (a +b+c) -a-b-c=3(a +b)(6 +c)(c +a) <br> 28. Simplify: <br> Simplify: (* + y)-(* -) -6y(* +y)(* - y) <br> <0. Without actual division, prove that 2x4-5x +2x 2-x +2 is divisible by x -3x +2. <br> 27. Simplify: (3x +4y) -(3x -4y) <br> (a) 1.01 0010001 <br> triangle. <br> triangle is less than the sum of three sides of the t <br> OR <br> 4/2 3V5 5/3 <br> V15 -3/2 V10-V3 V6 +V5 <br> (b) <br> + <br> 29. Classify the following numbers as rational or irrational with justification: <br> V28 <br> V343 <br> (c) 1.2555.. <br> OR <br> 31. Prove that if arms of an angle are respectively parallel to the arms of <br> another angle, then the angles are either equal or supplementary. <br> In AABC(Fig. 6), the sides AB and ACofAABC are produced to points E <br> and D respectively. If bisectors BO and CO of ZCBE and ZBCD <br> respectively meet at point 0, then prove that ZBOC = 90°-LA. <br> 2 <br> D <br> 32. Side BC ofa AABC is produced to a point D. The bisector ofZA meets BC <br> at L. Prove that ZABC +LACD =2/ALC. <br> E <br> 30. Three vertices of a rectangle are (-2, -5), (6, -5) and (6, -1). Plot these points and find the <br> Coordinates of the fourth vertex. Also find its area. <br> BA <br> Fig. 5 <br> (d) 1.350355035550... <br> A <br> A <br> Fig. 6 <br> 33. Prove that the angles opposite to equal sides ofan isosceles triangle are equal. Using the above, find 2B <br> in AABC with AC = BC in which ZC =50°. <br> 34. Ina right triangle, prove that the line segment joining the mid-point of the hypotenuse to the opposite <br> vertex is half the hypotenuse. <br>